Question

Geometry! Find the length of a-b. Give answer in simplest radical form.

Answer 1

Length of AB is
`√(106)`

Explanation:

Let us use the rule of the distance To find the length of AB

∵ A = (9, -3)

∵ B = (0, 2)

∴ x1 = 9 and y1 = -3

∴ x2 = 0 and y2 = 2

∵ AB =
`\sqrt{(x2-x1)^(2)+(y2-y1)^(2)}`

→ Substitute the values of x1, x2, y1, and y2 in the rule to find AB

∴ AB =
`\sqrt{(0-9)^(2)+(2--3)^(2)}`

∴ AB =
`\sqrt{(-9)^(2)+(2+3)^(2)}`

∴ AB =
`\sqrt{81+(5)^(2)}`

∴ AB =
`√(81+25)`

∴ AB =
`√(106)`

→ The square root of 106 is the simplest radical form

∴ Length of AB is
`√(106)`